Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-4y &= -6 \\ -5x+2y &= -2\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = 5x-2$ Divide both sides by $2$ to isolate $y$ $y = {\dfrac{5}{2}x - 1}$ Substitute this expression for $y$ in the first equation. $4x-4({\dfrac{5}{2}x - 1}) = -6$ $4x - 10x + 4 = -6$ Simplify by combining terms, then solve for $x$ $-6x + 4 = -6$ $-6x = -10$ $x = \dfrac{5}{3}$ Substitute $\dfrac{5}{3}$ for $x$ back into the top equation. $4( \dfrac{5}{3})-4y = -6$ $\dfrac{20}{3}-4y = -6$ $-4y = -\dfrac{38}{3}$ $y = \dfrac{19}{6}$ The solution is $\enspace x = \dfrac{5}{3}, \enspace y = \dfrac{19}{6}$.